On a class of nonlinear wave equations related to the Dirac-Klein-Gordon system with generalized Yukawa interaction
The author studies local low regularity solutions without any smallness assumption on the data of nonlinear wave equations of the form \(\square u=u^kDu,\) where \(Du\) stands for any of the first order derivatives \(\partial_tu,\;\partial_{x_j}u,\;i=1,2,3\) with initial data \(u(0,\cdot)=f\in H^s(\mathbb{R}^{3}),\;u_t(0,\cdot)=g\in H^{s-1}(\mathbb{R}^{3}).\) Local existence for large data in both the subcritical and critical cases and global existence for small data in the critical cases are proved. The motivation of this study is the following Dirac-Klein-Gordon system with generalized Yukawa interaction \(\mathcal{D}\psi=\varphi(\overline{\psi}\psi)^{\alpha}\psi,\;\square \varphi=(\overline{\psi}\psi)^{\beta},\) to which the obtained results are applied.
scientific article; zbMATH DE number 5076736
scientific article